Algebra Examples

$y = \frac{5}{2} x - 1$ $y = \frac{7}{2} x - 3$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{5}{2} x - 1 = \frac{7}{2} x - 3$

Step 2

Solve $\frac{5}{2} x - 1 = \frac{7}{2} x - 3$ for $x$ .

Tap for more steps...

Step 2.1

Combine $\frac{5}{2}$ and $x$ .

$\frac{5 x}{2} - 1 = \frac{7}{2} x - 3$

Step 2.2

Combine $\frac{7}{2}$ and $x$ .

$\frac{5 x}{2} - 1 = \frac{7 x}{2} - 3$

Step 2.3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.3.1

Subtract $\frac{7 x}{2}$ from both sides of the equation.

$\frac{5 x}{2} - 1 - \frac{7 x}{2} = - 3$

Step 2.3.2

Combine the numerators over the common denominator.

$- 1 + \frac{5 x - 7 x}{2} = - 3$

Step 2.3.3

Subtract $7 x$ from $5 x$ .

$- 1 + \frac{- 2 x}{2} = - 3$

Step 2.3.4

Cancel the common factor of $- 2$ and $2$ .

Tap for more steps...

Step 2.3.4.1

Factor $2$ out of $- 2 x$ .

$- 1 + \frac{2 (- x)}{2} = - 3$

Step 2.3.4.2

Cancel the common factors.

Tap for more steps...

Step 2.3.4.2.1

Factor $2$ out of $2$ .

$- 1 + \frac{2 (- x)}{2 (1)} = - 3$

Step 2.3.4.2.2

Cancel the common factor.

$- 1 + \frac{2 (- x)}{2 \cdot 1} = - 3$

Step 2.3.4.2.3

Rewrite the expression.

$- 1 + \frac{- x}{1} = - 3$

Step 2.3.4.2.4

Divide $- x$ by $1$ .

$- 1 - x = - 3$

Step 2.4

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.4.1

Add $1$ to both sides of the equation.

$- x = - 3 + 1$

Step 2.4.2

Add $- 3$ and $1$ .

$- x = - 2$

Step 2.5

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Tap for more steps...

Step 2.5.1

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Step 2.5.2

Simplify the left side.

Tap for more steps...

Step 2.5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Step 2.5.2.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Step 2.5.3

Simplify the right side.

Tap for more steps...

Step 2.5.3.1

Divide $- 2$ by $- 1$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Tap for more steps...

Step 3.1

Substitute $2$ for $x$ .

$y = \frac{7}{2} \cdot (2) - 3$

Step 3.2

Substitute $2$ for $x$ in $y = \frac{7}{2} \cdot (2) - 3$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Multiply $\frac{7}{2}$ by $2$ .

$y = \frac{7}{2} \cdot 2 - 3$

Step 3.2.2

Simplify $\frac{7}{2} \cdot 2 - 3$ .

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$y = \frac{7}{2} \cdot 2 - 3$

Step 3.2.2.1.2

Rewrite the expression.

$y = 7 - 3$

Step 3.2.2.2

Subtract $3$ from $7$ .

$y = 4$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 4)$

Equation Form:

$x = 2, y = 4$

Step 6